Papers from Acta

November 15, 2010

[1] A quantitative and thermodynamically consistent phase-field interpolation function for multi-phase systems

N Moelans

The aimed properties of the interpolation functions used in quantitative phase-field models for two-phase systems do not extend to multi-phase systems. Therefore, a new type of interpolation functions is introduced that has a zero slope at the equilibrium values of the non-conserved field variables representing the different phases and allows for a thermodynamically consistent interpolation of the free energies. The interpolation functions are applicable for multi-phase-field and multi-order-parameter representations and can be combined with existing quantitative approaches for alloys. A model for polycrystalline, multi-component and multi-phase systems is formulated using the new interpolation functions that accounts in a straightforward way for composition-dependent expressions of the bulk Gibbs energies and diffusion mobilities, and interfacial free energies and mobilities. The numerical accuracy of the approach is analyzed for coarsening and diffusion-controlled parabolic growth in Cu–Sn systems as a function of R/ℓ, with R grain size and ℓ diffuse interface width.

[2] On the analytical solution for self-similar grain size distributions in two dimensions

C S Pande and K P Cooper

In a recent publication an analytical solution of the Fokker–Planck continuity equation for the grain size distribution for two-dimensional grain growth in the long time limit (self-similar state) was provided. It used von Neumann–Mullins law and the results of Rios and Glicksman, but was based on a stochastic formulation first proposed by Pande. In this paper this analytical solution is compared with experimental and computer simulation distributions. It is found that grain size distribution, as obtained by simulations of two-dimensional grain growth, although in agreement with our analytical results, may in fact differ from experimentally obtained grain size distributions in thin films. It is also shown mathematically that in the two limiting cases the general solution is reduced to the Hillert or Rayleigh distributions.

[3] Morphological evolution and growth mechanism of primary Mg2Si phase in Al–Mg2Si alloys

C Li et al

Three-dimensional morphologies of primary Mg2Si in Al–Mg2Si alloys were studied in detail using field emission scanning electron microscopy, and its growth mechanism was also discussed. Primary Mg2Si crystals in the alloys display various geometric shapes, such as octahedron, hopper, truncated octahedron, cube and enormous dendrite, although they tend to form faceted octahedron (equilibrium shape) with minimized total surface free energy. The higher growth rate along left angle bracket1 0 0right-pointing angle bracket induces the degradation of the six {1 0 0} facets to corners, while eight {1 1 1} facets remain to form octahedron Mg2Si because of their lower growth rates. However, the growth velocities of the left angle bracket1 0 0right-pointing angle bracket and left angle bracket1 1 1right-pointing angle bracket directions can be manipulated by means of external growth conditions, which are responsible for the evolution of Mg2Si crystals into other morphologies.

[4] Elongated nanoscale voids at deformed special grain boundary structures in nanocrystalline materials

I A Ovid’ko et al

A special micromechanism for the formation of elongated nanoscale voids at grain boundaries (GBs) in deformed nanocrystalline materials is suggested and theoretically described. Within our description, the formation of nanoscale voids represents a slow (diffusion-controlled) process driven by release of the elastic energy of GB disclination configurations formed due to GB sliding. It is demonstrated that the nucleation of elongated nanoscale voids at GB disclination dipoles occurs as an energetically favorable process in deformed nanocrystalline Ni and Al2O3 (sapphire) in wide ranges of their parameters.

[5] A new framework for computationally efficient structure–structure evolution linkages to facilitate high-fidelity scale bridging in multi-scale materials models

T Fast et al

A novel mathematical framework called materials knowledge systems (MKS) was recently formulated to extract, store and recall computationally efficient hierarchical linkages that are at the core of multi-scale modeling of materials phenomena. A salient feature of this new framework is that it facilitates flow of high-fidelity information in both directions between the constituent length scales, and thereby offers a new strategy for concurrent multi-scale modeling. The viability of this new framework has thus far been largely explored for capturing the mechanical response of composite material systems. This paper extends the MKS framework to applications involving microstructure evolution, where the local states are typically defined in a continuous local state space. In particular, it will be shown that it is possible to obtain an efficient discretization of the local state space to produce a sufficiently accurate description of the linearized structure–structure evolution linkages for modeling spinodal decomposition. Furthermore, it will be shown that these linkages can be used successfully to accurately predict the continuous evolution of microstructure over the long time periods involved in such problems.

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